In this article, we show the existence of positive solution to nonlocal system $$\displaylines{ (-\Delta)^s u +a(x)u=\frac{1}{2_s^*} H_u(u,v) \quad \hbox{in }\mathbb{R}^N,\cr v +b(x)v=\frac{1}{2_s^*}H_v(u,v) } \mathbb{R}^N,\cr u,v>0 \text{in u,v\in \mathcal{D}^{s,2 }(\mathbb{R}^N). }$$ We also prove a global compactness result for associated energy functionalsimilar that due Struwe in [26]. ...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

We prove estimates of Calderón-Zygmund type for evolutionary pLaplacian systems in the setting of Lorentz spaces. We suppose the coefficients of the system to satisfy only a VMO condition with respect to the space variable. Our results hold true, mutatis mutandis, also for stationary p-Laplacian systems. PUBLISHED IN J. Differential Equations 255 (9): 2927–2951, 2013

We study the Nehari manifold for a class of quasilinear elliptic systems involving a pair of (p,q)-Laplacian operators and a parameter. We prove the existence of a nonnegative nonsemitrivial solution for the systems by discussing properties of the Nehari manifold, and so global bifurcation results are obtained. Thanks to Picone’s identity, we also prove a nonexistence result.

This paper discusses the implementation of several edge recognition systems: Sobel; Laplacian of Gaussian; and Canny, on commerically available Datacube MaxVideo image-processing hardware at or near frame rate. Any approximations necessary to operate at these throughput rates are described and a comparison made between the output of these systems and slower implementations on general-purpose ma...